Corrector theory for MsFEM and HMM in random media

We analyze the random fluctuations of several multi-scale algorithms such as the multi-scale finite element method (MsFEM) and the finite element heterogeneous multiscale method (HMM), that have been developed to solve partial differential equations with highly heterogeneous coefficients. Such multi-scale algorithms are often shown to correctly capture the homogenization limit when the highly oscillatory random medium is stationary and ergodic. This paper is concerned with the random fluctuations of the solution about the deterministic homogenization limit. We consider the simplified setting of the one dimensional elliptic equation, where the theory of random fluctuations is well understood. We develop a fluctuation theory for the multi-scale algorithms in the presence of random environments with short-range and long-range correlations. What we find is that the computationally more expensive method MsFEM captures the random fluctuations both for short-range and long-range oscillations in the medium. The less expensive method HMM correctly captures the fluctuations for long-range oscillations and strongly amplifies their size in media with short-range oscillations. We present a modified scheme with an intermediate computational cost that captures the random fluctuations in all cases.Comment: 41 page

Inverse Scattering and Acousto-Optic Imaging

We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes use of the principle of interior control of boundary measurements by an external wave field.Comment: 10 page

Inverse Diffusion Theory of Photoacoustics

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by high frequency radiation propagating inside a domain of interest. These data are obtained by solving an inverse wave equation, which is well-studied in the literature. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determines two constitutive parameters in diffusion and Schroedinger equations. Stability of the reconstruction is guaranteed under additional geometric constraints of strict convexity. No geometric constraints are necessary when $2n$ internal data for well-chosen boundary conditions are available, where $n$ is spatial dimension. The set of well-chosen boundary conditions is characterized in terms of appropriate complex geometrical optics (CGO) solutions.Comment: 24 page

Radiation- and Phonon-Bottleneck-Induced Tunneling in the Fe8 Single-Molecule Magnet

We measure magnetization changes in a single crystal of the single-molecule magnet Fe8 when exposed to intense, short (<20 $\mu$s) pulses of microwave radiation resonant with the m = 10 to 9 transition. We find that radiation induces a phonon bottleneck in the system with a time scale of ~5 $\mu$s. The phonon bottleneck, in turn, drives the spin dynamics, allowing observation of thermally assisted resonant tunneling between spin states at the 100-ns time scale. Detailed numerical simulations quantitatively reproduce the data and yield a spin-phonon relaxation time of T1 ~ 40 ns.Comment: 6 RevTeX pages, including 4 EPS figures, version accepted for publicatio

Low temperature microwave emission from molecular clusters

We investigate the experimental detection of the electromagnetic radiation generated in the fast magnetization reversal in Mn12-acetate at low temperatures. In our experiments we used large single crystals and assemblies of several small single crystals of Mn12-acetate placed inside a cylindrical stainless steel waveguide in which an InSb hot electron device was also placed to detect the radiation. All this was set inside a SQUID magnetometer that allowed to change the magnetic field and measure the magnetic moment and the temperature of the sample as the InSb detected simultaneously the radiation emitted from the molecular magnets. Our data show a sequential process in which the fast inversion of the magnetic moment first occurs, then the radiation is detected by the InSb device, and finally the temperature of the sample increases during 15 ms to subsequently recover its original value in several hundreds of milliseconds.Comment: changed conten

The effect of regular physical activity on women's self-confidence levels: An exploratory research

Introduction: It is known that physical activity is good for many diseases such as obesity, heart diseases, various types of cancer, musculoskeletal disorders. Compared to men, women's participation in physical activity is more limited. Physical activity, on the other hand, contributes to both the increase in the quality of life and the socialization of people. In this context, the aim of this study is to determine the self-confidence levels of women who regularly participate in physical activity. Method: In the research, besides the personal information form prepared by the researchers, the self-confidence scale was used. The sample population survey in Turkey Kocaeli province has created 408 women participating regularly in physical activity. In the analysis of the data, arithmetic means, frequency and percentage values were taken. As a result of the normality test, it was seen that it showed a normal distribution. Accordingly, independent sample t-test was used in the analysis of paired groups and one way Anova tests were used in the analysis of multiple groups. Results: As a result of the analysis, no significant difference was found in any sub-dimension according to the marital status variable. Significant differences were observed in the sub-dimensions of the scale according to the variables of income level, physical activity duration, education level and age. Conclusion: It has been observed that as the duration of physical activity increases, the level of self-confidence increases. In addition, it was concluded that age and educational status were directly related to self-confidence, and as education level and age increased, self-confidence increased

Coherent radiation by molecular magnets

The possibility of coherent radiation by molecular magnets is investigated. It is shown that to realize the coherent radiation, it is necessary to couple the considered sample to a resonant electric circuit. A theory for describing this phenomenon is developed, based on a realistic microscopic Hamiltonian, including the Zeeman terms, single-site anisotropy, and dipole interactions. The role of hyperfine interactions between molecular and nuclear spins is studied. Numerical solutions of the spin evolution equations are presented.Comment: Latex file, 11 pages, 3 figure

The role of inhibitory feedback for information processing in thalamocortical circuits

The information transfer in the thalamus is blocked dynamically during sleep, in conjunction with the occurence of spindle waves. As the theoretical understanding of the mechanism remains incomplete, we analyze two modeling approaches for a recent experiment by Le Masson {\sl et al}. on the thalamocortical loop. In a first step, we use a conductance-based neuron model to reproduce the experiment computationally. In a second step, we model the same system by using an extended Hindmarsh-Rose model, and compare the results with the conductance-based model. In the framework of both models, we investigate the influence of inhibitory feedback on the information transfer in a typical thalamocortical oscillator. We find that our extended Hindmarsh-Rose neuron model, which is computationally less costly and thus siutable for large-scale simulations, reproduces the experiment better than the conductance-based model. Further, in agreement with the experiment of Le Masson {\sl et al}., inhibitory feedback leads to stable self-sustained oscillations which mask the incoming input, and thereby reduce the information transfer significantly.Comment: 16 pages, 15eps figures included. To appear in Physical Review

Quantum Hall effect in InAsSb quantum wells at elevated temperatures

We have characterized the electronic properties of a high-mobility two-dimensional electron system in modulation doped InAsSb quantum wells and compare them to InSb quantum wells grown in a similar fashion. Using temperature-dependent Shubnikov-de Haas experiments as well as FIR transmission we find an effective mass of $m^{\ast} \approx$ 0.022$m_{e}$, which is lower than in the investigated InSb quantum well, but due to a rather strong confinement still higher than in the corresponding bulk compound. The effective $g$-factor was determined to be $g^{\ast} \approx$ 21.9. These results are also corroborated by $k \cdot p$ band structure calculations. When spin polarizing the electrons in a tilted magnetic field, the $g$-factor is significantly enhanced by electron-electron interactions, reaching a value as large as $g^{\ast}$ = 60 at a spin polarization P = 0.75. Finally, we show that due to the low effective mass the quantum Hall effect in our particular sample can be observed up to a temperature of 60 K and we propose scenarios how to increase this temperature even further.Comment: 12 pages, 15 figure